continuous linear operator or continuous linear mapping is a continuous linear transformation between topological vector spaces. An operator between two...

a linear endomorphism. Sometimes the term linear operator refers to this case, but the term "linear operator" can have different meanings for different...

analysis, a branch of mathematics, a closed linear operator or often a closed operator is a linear operator whose graph is closed (see closed graph property)...

In functional analysis and operator theory, a bounded linear operator is a linear transformation L : X → Y {\displaystyle L:X\to Y} between topological...

In mathematics, a differential operator is an operator defined as a function of the differentiation operator. It is helpful, as a matter of notation first...

the object. A projection on a vector space V {\displaystyle V} is a linear operator P : V → V {\displaystyle P\colon V\to V} such that P 2 = P {\displaystyle...

specifically in operator theory, each linear operator A {\displaystyle A} on an inner product space defines a Hermitian adjoint (or adjoint) operator A ∗ {\displaystyle...

finite-dimensional, then a linear operator L: V → W is continuous if and only if the kernel of L is a closed subspace of V. Consider a linear map represented as...

other examples) The most basic operators are linear maps, which act on vector spaces. Linear operators refer to linear maps whose domain and range are...

"operator" should be understood as "linear operator" (as in the case of "bounded operator"); the domain of the operator is a linear subspace, not necessarily the...

mathematics, the operator norm measures the "size" of certain linear operators by assigning each a real number called its operator norm. Formally, it...

the trace of a linear operator mapping a finite-dimensional vector space into itself, since all matrices describing such an operator with respect to...

In functional analysis, a branch of mathematics, a compact operator is a linear operator T : X → Y {\displaystyle T:X\to Y} , where X , Y {\displaystyle...

In mathematical analysis, an integral linear operator is a linear operator T given by integration; i.e., ( T f ) ( x ) = ∫ f ( y ) K ( x , y ) d y {\displaystyle...

Linear Operators is a three-volume textbook on the theory of linear operators, written by Nelson Dunford and Jacob T. Schwartz. The three volumes are...

In mathematics, the Laplace operator or Laplacian is a differential operator given by the divergence of the gradient of a scalar function on Euclidean...

mathematics, operator theory is the study of linear operators on function spaces, beginning with differential operators and integral operators. The operators may...

{\displaystyle f} is a bounded linear operator and so is continuous. In fact, to see this, simply note that f is linear, and therefore ‖ f ( x ) − f (...

mathematics (specifically linear algebra, operator theory, and functional analysis) as well as physics, a linear operator A {\displaystyle A} acting...

of two linear operators is a linear operator, as well as the product (on the left) of a linear operator by a differentiable function, the linear differential...

self-adjoint operator on a complex vector space V with inner product ⟨ ⋅ , ⋅ ⟩ {\displaystyle \langle \cdot ,\cdot \rangle } is a linear map A (from V...

time series analysis, the shift operator is called the lag operator. Shift operators are examples of linear operators, important for their simplicity...

linear operator on L1 is the convolution with a finite Borel measure. More generally, every continuous translation invariant continuous linear operator on...

functional analysis, a branch of mathematics, an operator algebra is an algebra of continuous linear operators on a topological vector space, with the multiplication...

functional analysis, the spectrum of a bounded linear operator (or, more generally, an unbounded linear operator) is a generalisation of the set of eigenvalues...

of the number of rows and columns, and the rank. The rank of a linear map or operator Φ {\displaystyle \Phi } is defined as the dimension of its image:...

upside-down triangle and pronounced "del", denotes the vector differential operator. When a coordinate system is used in which the basis vectors are not functions...

notation, also called Dirac notation, is a notation for linear algebra and linear operators on complex vector spaces together with their dual space both...

isomorphism between Hilbert spaces. Definition 1. A unitary operator is a bounded linear operator U : H → H on a Hilbert space H that satisfies U*U = UU*...

insights about an improved forward map. When operator F {\displaystyle F} is linear, the inverse problem is linear. Otherwise, that is most often, the inverse...